(1) Decision Efficiency in Football Passing: A Stable Player Metric from Probabilistic Option Sets

With Pedro Wightman and José Alejandro Guerrero.

Abstract. Football analytics has produced a substantial body of work on metrics that describe what happened on the pitch, but comparatively little on whether what happened represented a good choice among the alternatives available. This paper addresses that gap by reconstructing, for every pass in the 2022 FIFA World Cup, the set of alternatives the passer plausibly could have chosen instead. Using StatsBomb 360 freeze-frame data covering all 64 matches and 53,406 passes, an XGBoost model is trained to predict pass success from situational features alone (Area Under the ROC Curve (AUC) = 0.876, no player identity), and is applied to every visible teammate to construct a probabilistic option set for each pass. From these option sets, two complementary metrics are derived: Opportunity-Adjusted Risk-Taking (OART) and Decision Efficiency (DE). OART measures how much completion risk a player accepts relative to the safer alternatives that were available, where "safer" is defined by the model's estimated probability of completing the pass and retaining possession. DE measures how consistently a player selects the option with the highest estimated completion probability among those available. Applying the same reliability analysis to both, the intraclass correlation coefficient (ICC), the share of variance attributable to differences between players, is 0.010 (95% CI [0.007, 0.013]) for OART and 0.049 (95% CI [0.041, 0.058]) for DE; the split-half reliability of DE is r = 0.578. For OART, the remaining variance is dominated by the tactical configuration at the moment of the pass, so OART is most informative when read as a property of situations and is sensitive to context such as whether a team is pressing or building play near its own box. DE, by contrast, recovers a more stable player-level signal: in the most heterogeneous decile of option sets, where players face genuinely different choices, its ICC rises to 11.5%. Both metrics carry practical value at the event level: in the attacking third, high-OART passes are associated with roughly 1.7 times the expected goals (xG) of low-OART passes (p < 0.001), so situational risk-taking, when it occurs where it can matter, is associated with measurably better chance creation.

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(2) Structural Constraints on Information Aggregation in Directed Networks

Abstract. This paper investigates how the topological structure of directed networks constrains the set of outcomes achievable under local, decentralized information dynamics. Rather than asking what equilibrium a particular learning rule will reach, it asks a prior question: what outcomes are structurally impossible given only the network topology, regardless of the specific update rule employed? Through a combination of theoretical analysis and computational simulation across multiple network structures and update rules, it identifies conditions under which consensus is structurally precluded and characterize how the decomposition of a directed graph into strongly connected components shapes the space of possible asymptotic states. Results suggest that certain impossibility results are robust across a broad class of local averaging dynamics.

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